Strong CP problem and mirror world: the Weinberg–Wilczek axion revisited

A new possibility for solving the strong CP problem is suggested. It is based on the concept of a mirror world of particles, with the gauge symmetry and Lagrangian completely identical to that of the observable particles. We assume that the ordinary and mirror sectors share the same Peccei–Quinn symmetry realized à la Weinberg–Wilczek, so that the θ-terms are simultaneously canceled by the axion VEV in both worlds. This property remains valid even if the symmetry between two sectors is spontaneously broken and the weak scale of the mirror world is larger than the ordinary weak scale, in which case also the mirror QCD scale becomes larger than the ordinary one. In this situation our axion essentially represents a Weinberg–Wilczek axion of the mirror world with quite a large mass, while it couples the ordinary particles like an invisible axion. The experimental and astrophysical limits are discussed and an allowed parameter window is found with the Peccei–Quinn scale f_a10⁴–10⁵ GeV and the axion mass m_a1 MeV, which can be accessible for future experiments. We also show that our solution to the strong CP problem is stable against the Planck scale induced effects.     

A Pati–Salam model from branes

We explore the possibility of embedding the Pati–Salam model in the context of Type I brane models. We study a generic model with U(4)_C×U(2)_L×U(2)_R gauge symmetry and matter fields compatible with a Type I brane configuration. Examining the anomaly cancellation conditions of the surplus abelian symmetries we find an alternative hypercharge embedding that is compatible with a low string/brane scale of the order of 5–7 TeV, when the U(4)_C and U(2)_R brane stack couplings are equal. Proton stability is assured as baryon number is associated to a global symmetry remnant of the broken abelian factors. It is also shown that this scenario can accommodate an extra low energy abelian symmetry that can be associated to lepton number. The issue of fermion and especially neutrino masses is also discussed.     

Discrete gauge symmetry anomalies

It has been recently argued that quantum gravity effects strongly violate all non-gauge symmetries. This would suggest that all low energy discrete symmetries should be gauge symmetries, either continuous or discrete. Acceptable continuous gauge symmetries are constrained by the condition they should be anomaly free. We show here that any discrete gauge symmetry should also obey certain “discrete anomaly cancellation” conditions. These conditions strongly constrains the massles fermion content of the theory and follow from the “parent” cancellation of the usual continuous gauge anomalies. They have interesting applications in model building. As an example we consider the constraints on the Z_N “generalized matter parities” of the supersymmetric standard model. We show that only a few (including the standard R-parity) are “discrete anomaly free” unless the fermion content of the minimal supersymmetric standard model is enlarged.     

Discrete symmetry and GUT breaking

We study the supersymmetric GUT models in which the supersymmetry and GUT gauge symmetry can be broken by a discrete symmetry. First, with the ansatz that there exist discrete symmetries in the branes' neighborhoods, we discuss the general reflection symmetries and GUT breaking on and . In those models, the extra dimensions can be large and the KK states can be set arbitrarily heavy. Second, considering that the extra space manifold is the annulus or the disc , we can define any symmetry and break any 6-dimensional N=2 supersymmetric SU(M) models down to the 4-dimensional N=1 supersymmetric models for the zero modes. In particular, there might exist the interesting scenario on where just a few KK states are light, while the others are relatively heavy. Third, we discuss the complete global discrete symmetries on and study the GUT breaking. Received: 12 February 2002 / Published online: 14 June 2002     

Unified models at intermediate energy scales and Kaluza–Klein excitations

We discuss the possibility of intermediate gauge coupling unification in unified models of string origin. Useful relations of the β-function coefficients are derived, which ensure unification of couplings when Kaluza–Klein excitations are included above the compactification scale. We apply this procedure to two models with SU(3)×SU(3)_L×SU(3)_R and SU(4)×O(4) gauge symmetries.     

Domain wall solutions with Abelian gauge fields

We study kink (domain wall) solutions in a model consisting of two complex scalar fields coupled to two independent Abelian gauge fields in a Lagrangian that has U(1)×U(1) gauge plus discrete symmetry. We find consistent solutions such that while the U(1) symmetries of the fields are preserved while in their respective vacua, they are broken on the domain wall. The gauge field solutions show that the domain wall is sandwiched between domains with constant magnetic fields.     

QCD axion from a higher dimensional gauge field theory

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

Specific scalar mass relations in SU(3) × SU(2) × U(1) orbifold model

We study flat directions and soft scalar masses using a Z₃ orbifold model with SU(3) × SU(2) × U(1) gauge group and extra gauge symmetries including an anomalous U(1) symmetry. Soft scalar masses contain D-term contributions and particle mixing effects after symmetry breaking and they are parametrized by a few parameters. Some specific relations among scalar masses are obtained.     

Natural electroweak breaking from a mirror symmetry

We present "twin Higgs models," simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.     

Meeting the constraint of neutrino—Higgsino mixing in gravity unified theories

In gravity unified theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B - L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.     

The minimal axion minimal linear $$\sigma $$ model

The minimal SO(5) / SO(4) linear \(\sigma \) model is extended including an additional complex scalar field, singlet under the global SO(5) and the Standard Model gauge symmetries. The presence of this scalar field creates the conditions to generate an axion à la KSVZ, providing a solution to the strong CP problem, or an axion-like-particle. Different choices for the PQ charges are possible and lead to physically distinct Lagrangians. The internal consistency of each model necessarily requires the study of the scalar potential describing the \(SO(5)\rightarrow SO(4)\), electroweak and PQ symmetry breaking. A single minimal scenario is identified and the associated scalar potential is minimised including counterterms needed to ensure one-loop renormalizability. In the allowed parameter space, phenomenological features of the scalar degrees of freedom, of the exotic fermions and of the axion are illustrated. Two distinct possibilities for the axion arise: either it is a QCD axion with an associated scale larger than \(\sim 10^{5}\) TeV and therefore falling in the category of the invisible axions; or it is a more massive axion-like-particle, such as a 1 GeV axion with an associated scale of \(\sim 200\) TeV, that may show up in collider searches.     

Effect of bare mass on the Hosotani mechanism

It is pointed out that the existence of bare mass terms for matter fields changes gauge symmetry patterns through the Hosotani mechanism. As a demonstration, we study an SU(2) gauge model with massive adjoint fermions defined on M⁴S¹. It turns out that the vacuum structure changes at certain critical values of mL, where m (L) stands for the bare mass (the circumference of S¹). The gauge symmetry breaking patterns are different from models with massless adjoint fermions. We also consider a supersymmmetric SU(2) gauge model with adjoint hypermultiplets, in which the supersymmetry is broken by bare mass terms for the gaugino and squark fields instead of the Scherk–Schwarz mechanism.     

Freedom in electroweak symmetry breaking and mass matrix of fermions in dimensional deconstruction model

There exists a freedom in a class of four-dimensional electroweak theories proposed by Arkani-Hamed et al. relying on deconstruction and Coleman–Weinberg mechanism. The freedom comes from the winding modes of the link variable (Wilson operator) connecting non-nearest neighbours in the discrete fifth dimension. Using this freedom, dynamical breaking of SU(2) gauge symmetry, mass hierarchy patterns of fermions and Cabbibo–Kobayashi–Maskawa matrix may be obtained.     

Local grand unification in the heterotic landscape

We consider the possibility that the unification of the electroweak interactions and the strong force arises from string theory, at energies significantly lower than the string scale. As a tool, an effective grand unified field theory in six dimensions is derived from an anisotropic orbifold compactification of the heterotic string. It is explicitly shown that all anomalies cancel in the model, though anomalous Abelian gauge symmetries are present locally at the boundary singularities. In the supersymmetric vacuum additional interactions arise from higher‐dimensional operators. We develop methods that relate the couplings of the effective theory to the location of the vacuum, and find that unbroken discrete symmetries play an important role for the phenomenology of orbifold models. An efficient algorithm for the calculation of the superpotential to arbitrary order is developed, based on symmetry arguments. We furthermore present a correspondence between bulk fields of the orbifold model in six dimensions, and the moduli fields that arise from compactifying four internal dimensions on a manifold with non‐trivial gauge background.     

Flat directions,string compactification and three generation models

We show how identification of absolutely flat directions allows the construction of a new class of compactified string theories with reduced gauge symmetry that may or may not be continuously connected to the original theory. We use this technique to construct a class of three generation models with just the Standard Model gauge group after compactification. We discuss the low-energy symmetries necessary for a phenomenologically viable low-energy model and construct an example in which these symmetries are identified with string symmetries which remain unbroken down to the supersymmetry breaking scale. Remarkably the same symmetry responsible for stabilising the nucleon is also responsible for ensuring one and only one pair of Higgs doublets is kept light. We show how the string symmetries also lead to textures in the quark and lepton mass matrices which can explain the hierarchy of fermion masses and mixing angles.     

Variational formulation of Chern–Simons theory for arbitrary Lie groups

We show that the Chern–Simons theory for a principal G-bundle P over a three-dimensional manifold, with G an arbitrary Lie group, can be formulated as a variational problem defined by local data on the bundle of connections C(P) of P. By means of the theory of variational problems defined by local data we prove that the Euler–Lagrange operator and the differential of the Poincaré–Cartan form can be intrinsically expressed in terms of the symplectic form and the curvature morphism of C(P). These facts and the theory of the global inverse problem of the Calculus of Variations allow us to prove that there is indeed a global Lagrangian density for these theories. We also prove that every infinitesimal automorphism of P produces in a natural way an infinitesimal symmetry of the variational problem defined by the Chern–Simons theory. We therefore conclude that the algebra of infinitesimal symmetries of these theories is infinite dimensional.     

Chan–Paton soliton gauge states of the compactified open string

We study the mechanism of the enhanced gauge symmetry of the bosonic open string compactified on a torus by analyzing the zero-norm soliton (non-zero winding of the Wilson line) gauge states in the spectrum. Unlike the closed string case, we find that the soliton gauge state exists only at massive levels. These soliton gauge states correspond to the existence of enhanced massive gauge symmetries with transformation parameters containing both Einstein and Yang–Mills indices. In the T-dual picture, these symmetries exist only at some discrete values of compactified radii when N D-branes are coincident. Received: 14 May 1999 / Published online: 17 March 2000     

Local Cosmic Strings from Pseudo-Anomalous U(1)

Local cosmic strings solutions are introduced ina model with a peudo-anomalous U(1) gauge symmetry. Sucha symmetry is present in many superstringcompactification models. The coupling of those strings with the axion necessary in order to cancel theanomalies does not prevent them from being local, eventhough their energy per unit length is found to divergelogarithmically. I discuss briefly the formation of such strings and the phenomenologicalconstraints that apply to their parameters.     

On axionic dark matter in Type IIA string theory

We investigate viable scenarios with various axions in the context of supersymmetric field theory and in globally consistent D‐brane models. The Peccei‐Quinn symmetry is associated with an anomalous U(1) symmetry, which acquires mass at the string scale but remains as a perturbative global symmetry at low energies. The origin of the scalar Higgs‐axion potential from F‐, D‐ and soft breaking terms is derived, and two Standard Model examples of global intersecting D6‐brane models in Type II orientifolds are presented, which differ in the realisation of the Higgs sector and in the hidden sector, the latter of which is of particluar importance for the soft supersymmetry breaking terms.